Sidon Sets are Proportionally Sidon with Small Sidon Constants

Generalized Sidon sets

We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon. © 2010 Elsevier Inc. All rights reserved. MSC: 11B

Proportions of Sidon Sets Are I0 Subsets

It is proved that proportions of Sidon sets are I0 subsets of controlled degree. That is, a set E is Sidon if and only if, there are r > 0 and positive integer n such that, for every finite subset F ⊂ E, there is H ⊂ F with the cardinality of H at least r times the cardinality of F and N(H) ≤ n (N(H) is a measure of the degree of being I0). This paper leaves open David Grow’s question of whethe...

Sumsets of Sidon sets

Arithmetic Characterizations of Sidon Sets

Let G be any discrete Abelian group. We give several arithmetic characterizations of Sidon sets in G. In particular, we show that a set A is a Sidon set iff there is a number 6 > 0 such that any finite subset A of A contains a subset B Q A with |B| > 6\A\ which is quasiindependent, i.e. such that the only relation of the form ]C\eB e x ^ = '̂ with e\ equal to + 1 or 0, is the trivial one. Let G ...

On Uniformly Approximable Sidon Sets

Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...